Quantum Hall fractions in ultracold fermionic vapors

We study the quantum Hall states that appear in the dilute limit of rotating ultracold fermionic gases when a single hyperfine species is present. We show that the $p$-wave scattering translates into a pure hard-core interaction in the lowest Landau level. The Laughlin wave function is then the exact ground state at filling fraction $\nu =1∕3$. We give estimates of some of the gaps of the incompressible liquids for $\nu =p∕(2p\pm 1)$. We estimate the mass of the composite fermions at $\nu =1∕2$. The width of the quantum Hall plateaus is discussed by considering the equation of state of the system.

Figure 1

Energy gaps for neutral and charged excitations at $\nu =1∕3$, $\nu =2∕5$, and neutral gaps for $\nu =3∕7$. The lines are our best fits and energies are in units of $g_f$.

Figure 2

Energy spectrum for $N=9$ fermions in the spherical geometry at filling $\nu =1∕2$. The CFs feel zero flux and can be interpreted as forming a closed shell. The inset shows the scaling of the gap of the closed shell states $N=4$, 9, 16. Energies are in units of $g$ and the horizontal axis is total angular momentum.

Figure 3

Energy spectrum for $N=5$ fermions in the disk geometry as a function of the angular momentum. The Laughlin state is the unique zero-energy state at $L_z=30$. The lowest-energy state at $L_z=25$ is the quasielectron with a finite gap.